JEE Main 2019 12th April Morning Shift Question Paper with Solutions

The trajectory of a projectile near the surface of the earth is given as y = 2x – 9x² . If it were launched at an angle $\theta$₀ with speed v₀ then (g = 10 ms^–2) :

The value of numerical aperature of the objective lens of a microscope is 1.25. If light of wavelength 5000 $\mathop A\limits^o$ is used, the minimum separation between two points, to be seen as distinct, will be :

Two identical parallel plate capacitors, of capacitance C each, have plates of area A, separated by a distance d. The space between the plates of the two capacitors, is filled with three dielectrics, of equal thickness and dielectric constants K₁, K₂ and K₃. The first capacitor is filled as shown in fig.I, and the second one is filled as shown in fig II. If these two modified capacitors are charged by the same potential V, the ratio of the energy stored in the two, would be (E₁ refers to capacitor (I) and E₂ to capacitor (II)):

The transfer characteristic curve of a transistor, having input and output resistance 100 $\Omega$ and 100 k$\Omega$ respectively is shown in the figure. The voltage and power gain, are respectively:

The truth table for the circuit given in the fig. is:

A sample of an ideal gas is taken through the cyclic process abca as shown in the figure. The change in the internal energy of the gas along the path ca is –180 J. The gas absorbs 250 J of heat along the path ab and 60 J along the path bc. The work done by the gas along the path abc is:

To verify Ohm's law, a student connects the voltmeter across the battery as, shown in the figure. The measured voltage is plotted as a function of the current, and the following graph is obtained :
If V₀ is almost zero, identify the correct statement :

A man (mass = 50 kg) and his son (mass = 20 kg) are standing on a frictionless surface facing each other. The man pushes his son so that he starts moving at a speed of 0.70 ms^–1 with respect to the man. The speed of the man with respect to the surface is :

A person of mass M is, sitting on a swing of length L and swinging with an angular amplitude $\theta$₀. If the person stands up when the swing passes through its lowest point, the work done by him, assuming that his center of mass moves by a distance $\ell$($\ell$ << L), is close to;

A thin ring of 10 cm radius carries a uniformly distributed charge. The ring rotates at a constant angular speed of 40 $\pi$ rad s^–1 about its axis, perpendicular to its plane. If the magnetic field at its centre is 3.8 × 10^–9 T, then the charge carried by the ring is close to ($\mu$₀ = 4$\pi$ × 10^–7 N/A² ).

An excited He⁺ ion emits two photons in succession, with wavelengths 108.5 nm and 30.4 nm, in making a transition to ground state. The quantum number n, corresponding to its initial excited state is (for photon of wavelength $\lambda$, energy $E = {{1240\,eV} \over {\lambda (in\,nm)}}$) :

At 40^o C, a brass wire of 1 mm radius is hung from the ceiling. A small mass, M is hung from the free end of the wire. When the wire is cooled down from 40^oC to 20^oC it regains its original length of 0.2 m. The value of M is close to : (Coefficient of linear expansion and Young’s modulus of brass are 10^–5 /^oC and 10¹¹ N/m ² , respectively; g= 10 ms^–2 )

A magnetic compass needle oscillates 30 times per minute at a place where the dip is 45^o, and 40 times per minute where the dip is 30^o. If B₁ and B₂ are respectively the total magnetic field due to the earth at the two places, then the ratio ${{{B_1}} \over {{B_2}}}$ is best given by :

A galvanometer of resistance 100 $\Omega$ has 50 divisions on its scale and has sensitivitv of 20 $\mu$A/division. It is to be converted to a voltmeter with three ranges of 0-2V, 0-10 V and 0-20 V. The appropriate circuit to do so is

The resistive network shown below is connected to a D.C. source of 16 V. The power consumed by the network is 4 Watt. The value of R is:

The stopping potential V₀ (in volt) as a function of frequency ($\upsilon$) for a sodium emitter, is shown in the figure. The work function of sodium, from the data plotted in the figure, will be:
(Given: Planck’s constant (h) = 6.63 × 10^–34 Js, electron charges e = 1.6 × 10^–19 C)

A concave mirror has radius of curvature of 40 cm. It is at the bottom of a glass that has water filled up to 5 cm (see figure). If a small particle is floating on the surface of water, its image as seen, from directly above the glass, is at a distance d from the surface of water. The value of d is dose to: (Refractive index of water = 1.33)

A circular disc of radius b has a hole of radius a at its centre (see figure). If the mass per unit area of the disc varies as $\left( {{{{\sigma _0}} \over r}} \right)$ , then the radius of gyration of the disc about its axis passing through the centre is:

A shell is fired from a fixed artillery gun with an initial speed u such that it hits the target on the ground at a distance R from it. If t₁ and t₂ are the values of the time taken by it to hit the target in two possible ways, the product t₁t₂ is -

When M₁ gram of ice at –10^oC (specific heat = 0.5 cal g^{–1 o}C^–1 ) is added to M₂ gram of water at 50C, finally no ice is left and the water is at 0°C. The value of latent heat of ice, in cal g^–1 is :

In a double slit experiment, when a thin film of thickness t having refractive index $\mu$. is introduced in front of one of the slits, the maximum at the centre of the fringe pattern shifts by one fringe width. The value of t is ($\lambda$ is the wavelength of the light used) :

The figure shows a square loop L of side 5 cm which is connected to a network of resistances. The whole setup is moving towards right with a constant speed of 1 cm s^-1. At some instant, a part of L is in a uniform magnetic field of 1 T, perpendicular to the plane of the loop. If the resistance of L is 1.7 $\Omega$, the current in the loop at that instant will be close to :

A uniform rod of length $\ell$ is being rotated in a horizontal plane with a constant angular speed about an axis passing through one of its ends. If the tension generated in the rod due to rotation is T(x) at a distance x from the axis, then which of the following graphs depicts it most closely?

A progressive wave travelling along the positive x-direction is represented by y(x,t) = Asin(kx – $\omega$t + $\phi$). Its snapshot at t = 0 is given in the figure.
For this wave, the phase $\phi$ is :

Shown in the figure is a shell made of a conductor. It has inner radius a and outer radius b, and carries charge Q. At its centre is a dipole $\overrightarrow P$ as shown. In this case :

A submarine (A) travelling at 18 km/hr is being chased along the line of its velocity by another submarine (B) travelling at 27 km/hr. B sends a sonar signal of 500 Hz to detect A and receives a reflected sound of frequency $\upsilon$. The value of $\upsilon$ is close to: (Speed of sound in water =1500 ms^–1)

Which of the following combinations has the dimension of electrical resistance ($\in$₀ is the permittivity of vacuum and $\mu$₀ is the permeability of vacuum)?

Two moles of helium gas is mixed with three moles of hydrogen molecules (taken to be rigid). What is the molar specific heat of mixture at constant volume ? (R = 8.3 J/mol K)

A point dipole $\overrightarrow p = - {p_0}\widehat x$ is kept at the origin. The potential and electric field due to this dipole on the y-axis at a distance d are, respectively: (Take V= 0 at infinity)

An electromagnetic wave is represented by the electric field $\overrightarrow E = {E_0}\widehat n\sin \left[ {\omega t + \left( {6y - 8z} \right)} \right]$ . Taking unit vectors in x, y and z directions to be $\widehat i,\widehat j,\widehat k$ , the direction of propagation $\widehat s$, is :

The metal that gives hydrogen gas upon treatment with both acid as well as base is :

But-2-ene on reaction with alkaline KMnO₄ at elevated temperature followed by acidification will give :

Peptization is a :

The major product of the following addition reaction is :
H₃C–CH=CH₂ $\buildrel {C{l_2}/{H_2}O} \over \longrightarrow$

An organic compound 'A' is oxidizod with Na₂O₂ followed by boiling with HNO₃. The resultant solution is then treated with ammonium molybdate to yield a yellow precipitate.
Based on above observation, the element present in the given compound is:

The major products of the following reaction are :

In the following reaction; xA $\to$ yB
${\log _{10}}\left[ { - {{d\left[ A \right]} \over {dt}}} \right] = {\log _{10}}\left[ {{{d\left[ B \right]} \over {dt}}} \right] + 0.3010$
'A' and 'B' respectively can be :

The correct set of species responsible for the photochemical smog is :

Complete removal of both the axial ligands (along the z-axis) from an octahedral complex leads to which of the following splitting patterns? (relative orbital energies not on scale).

The electrons are more likely to be found :

The correct sequence of thermal stability of the following carbonates is :

Which of the following statements is not true about RNA?

The basic structural unit of feldspar, zeolites, mica, and asbestos is :

Enthalpy of sublimation of iodine is 24 cal g^–1 at 200 ^oC. If specific heat of I₂(s) and l₂ (vap) are 0.055 and 0.031 cal g^–1K ^–1 respectively, then enthalpy of sublimation of iodine at 250 ^oC in cal g^–1 is :